int mpz_probab_prime_p (mpz_srcptr n, int reps) { mp_limb_t r; mpz_t n2; /* Handle small and negative n. */ if (mpz_cmp_ui (n, 1000000L) <= 0) { if (mpz_cmpabs_ui (n, 1000000L) <= 0) { int is_prime; unsigned long n0; n0 = mpz_get_ui (n); is_prime = n0 & (n0 > 1) ? isprime (n0) : n0 == 2; return is_prime ? 2 : 0; } /* Negative number. Negate and fall out. */ PTR(n2) = PTR(n); SIZ(n2) = -SIZ(n); n = n2; } /* If n is now even, it is not a prime. */ if (mpz_even_p (n)) return 0; #if defined (PP) /* Check if n has small factors. */ #if defined (PP_INVERTED) r = MPN_MOD_OR_PREINV_MOD_1 (PTR(n), (mp_size_t) SIZ(n), (mp_limb_t) PP, (mp_limb_t) PP_INVERTED); #else r = mpn_mod_1 (PTR(n), (mp_size_t) SIZ(n), (mp_limb_t) PP); #endif if (r % 3 == 0 #if GMP_LIMB_BITS >= 4 || r % 5 == 0 #endif #if GMP_LIMB_BITS >= 8 || r % 7 == 0 #endif #if GMP_LIMB_BITS >= 16 || r % 11 == 0 || r % 13 == 0 #endif #if GMP_LIMB_BITS >= 32 || r % 17 == 0 || r % 19 == 0 || r % 23 == 0 || r % 29 == 0 #endif #if GMP_LIMB_BITS >= 64 || r % 31 == 0 || r % 37 == 0 || r % 41 == 0 || r % 43 == 0 || r % 47 == 0 || r % 53 == 0 #endif ) { return 0; } #endif /* PP */ /* Do more dividing. We collect small primes, using umul_ppmm, until we overflow a single limb. We divide our number by the small primes product, and look for factors in the remainder. */ { unsigned long int ln2; unsigned long int q; mp_limb_t p1, p0, p; unsigned int primes[15]; int nprimes; nprimes = 0; p = 1; ln2 = mpz_sizeinbase (n, 2); /* FIXME: tune this limit */ for (q = PP_FIRST_OMITTED; q < ln2; q += 2) { if (isprime (q)) { umul_ppmm (p1, p0, p, q); if (p1 != 0) { r = MPN_MOD_OR_MODEXACT_1_ODD (PTR(n), (mp_size_t) SIZ(n), p); while (--nprimes >= 0) if (r % primes[nprimes] == 0) { ASSERT_ALWAYS (mpn_mod_1 (PTR(n), (mp_size_t) SIZ(n), (mp_limb_t) primes[nprimes]) == 0); return 0; } p = q; nprimes = 0; } else { p = p0; } primes[nprimes++] = q; } } } /* Perform a number of Miller-Rabin tests. */ return mpz_millerrabin (n, reps); }
int mpz_probab_prime_p (mpz_srcptr n, int reps) { mp_limb_t r; /* Handle small and negative n. */ if (mpz_cmp_ui (n, 1000000L) <= 0) { int is_prime; if (mpz_sgn (n) < 0) { /* Negative number. Negate and call ourselves. */ mpz_t n2; mpz_init (n2); mpz_neg (n2, n); is_prime = mpz_probab_prime_p (n2, reps); mpz_clear (n2); return is_prime; } is_prime = isprime (mpz_get_ui (n)); return is_prime ? 2 : 0; } /* If n is now even, it is not a prime. */ if ((mpz_get_ui (n) & 1) == 0) return 0; #if defined (PP) /* Check if n has small factors. */ #if defined (PP_INVERTED) r = MPN_MOD_OR_PREINV_MOD_1 (PTR(n), SIZ(n), (mp_limb_t) PP, (mp_limb_t) PP_INVERTED); #else r = mpn_mod_1 (PTR(n), SIZ(n), (mp_limb_t) PP); #endif if (r % 3 == 0 #if BITS_PER_MP_LIMB >= 4 || r % 5 == 0 #endif #if BITS_PER_MP_LIMB >= 8 || r % 7 == 0 #endif #if BITS_PER_MP_LIMB >= 16 || r % 11 == 0 || r % 13 == 0 #endif #if BITS_PER_MP_LIMB >= 32 || r % 17 == 0 || r % 19 == 0 || r % 23 == 0 || r % 29 == 0 #endif #if BITS_PER_MP_LIMB >= 64 || r % 31 == 0 || r % 37 == 0 || r % 41 == 0 || r % 43 == 0 || r % 47 == 0 || r % 53 == 0 #endif ) { return 0; } #endif /* PP */ /* Do more dividing. We collect small primes, using umul_ppmm, until we overflow a single limb. We divide our number by the small primes product, and look for factors in the remainder. */ { unsigned long int ln2; unsigned long int q; mp_limb_t p1, p0, p; unsigned int primes[15]; int nprimes; nprimes = 0; p = 1; ln2 = mpz_sizeinbase (n, 2) / 30; ln2 = ln2 * ln2; for (q = PP_FIRST_OMITTED; q < ln2; q += 2) { if (isprime (q)) { umul_ppmm (p1, p0, p, q); if (p1 != 0) { r = mpn_mod_1 (PTR(n), SIZ(n), p); while (--nprimes >= 0) if (r % primes[nprimes] == 0) { ASSERT_ALWAYS (mpn_mod_1 (PTR(n), SIZ(n), (mp_limb_t) primes[nprimes]) == 0); return 0; } p = q; nprimes = 0; } else { p = p0; } primes[nprimes++] = q; } } } /* Perform a number of Miller-Rabin tests. */ return mpz_millerrabin (n, reps); }